Media reports treated last week's poll of Iraqis, commissioned by the BBC, ABC News and others, as the population's definitive word on the war. "Iraqis happier without Saddam" trumpeted headlines, in response to the claim that 57% think life is better now than it was before the war. The poll of 2,737 Iraqis was carried out in February by Oxford Research International (ORI), which describes it as "a national survey" and "representative". President Bush's official blog gave it an approving nod: "Thanks to the bravery of our troops, and the principled, consistent leadership of our president, we are leaving Iraq better than we found it."

But how representative of Iraqi views is it? Western companies have conducted polls, but their findings are unconvincing. In October Zogby International and the American Enterprise magazine said they had conducted "the first scientific poll of the Iraqi public". Yet their sample was small: 600 Iraqis in Basra, Mosul, Kirkuk and Ramadi.

Polling in any post-war setting is difficult, and there are additional problems in Iraq. The UN says there is "a dearth of demographic information about Iraq's population over the past several decades". As a consequence of Ba'ath party secrecy, questions remain about the distribution of ethnic and religious groups and social classes. Iain Murray, a statistician based in Washington, says that for a poll to be representative, "matching the sample to the country's demography is absolutely key. Otherwise, you simply cannot be sure that you are not weighting the sample unconsciously towards or away from any section of society."

So how did ORI weight its sample for class and religion, to achieve results that, according to the BBC, "reflected Iraq's distribution of population, balance between men and women, and religious and ethnic mix"? It didn't. Director Christoph Sahm said it weighted by governorate (Iraq's 18 regions), by distribution between urban and rural areas, and by age. So there was no weighting by social factors? "How would you do that?" he says. "How would you know what the breakdown is? No one knows."

Doesn't this present a problem for pollsters - that "no one knows" the basic facts about the make-up of the Iraqi population? In ORI's poll, 44% identified themselves as Sunni Muslim and 33% as Shia - yet, according to other accounts, Sunnis are a minority and Shias a majority. Sahm says this disparity is not a result of unconscious weighting, but of "prestige bias" by Iraqis. "In Saddam's Iraq, Sunni was seen as more prestigious than Shia."

If a large number of respondents answered questions about religion according to what was "prestigious", perhaps they answered others according to what was previously expected - that you should give a positive appraisal of the powers-that-be. Sahm says the poll was representative because it was "entirely random" and that every resident aged 15 or over had an equal chance of being selected. Working from the 1997 census and, where possible, from UN data, ORI targeted administrative units in descending order of size, and allocated interviews in each unit proportionate to population size. On the ground, households were targeted by "random route, random interval procedures".

Yet such polls require good demographic material from which to select - ideally a census. The 1997 census is widely viewed as being of poor quality and covered only 15 of Iraq's 18 governorates, excluding those that had become autonomous Kurdish territory in 1991; it was conducted during the era of sanctions; and seems to have been a bit of a rush job.

It remains questionable whether you can conduct a representative poll in a country that lacks demographic data and where instability is rife. ORI's poll does not cover all aspects of postwar Iraq. It asks whether Iraqis have had an encounter with coalition forces, and when they think they should leave, but it does not ask about their day-to-day experience or political view of the occupation. Sahm says "there was no room for that", and some media groups that commissioned the poll "did not want a question about the occupation".

Many of the media reports about "happy Iraqis" focused on question two, which asked: "Compared to a year ago, I mean before the war in spring 2003, [how] are things overall in your life?": 21.9% said "much better now"; 34.6% said "somewhat better"; 23.3% said "about the same"; 12.7% said "somewhat worse"; and 5.9% said "much worse". This is where the headline figure of 57% comes from - those who reportedly think Iraq is a better place.

Yet on the specifics, Iraqis appear less optimistic: when asked about their neighbourhoods, 68.6% think the availability of jobs is bad, compared with 25.6% who think it is good, 64.4% think the supply of electricity supply is bad, while 34.9% think it is good, 50.1% think the security situation is bad, compared with 48.9% who think it is good. A majority believe public provision has at best remained the same, or got worse; only on security and crime do most think there has been an improvement.

The poll also fails to take into account the UN's lifting of sanctions in May. These restricted access to food, medicine and basic materials. Perhaps it was the end of sanctions, more than the end of Saddam, that improved Iraqis' "day-to-day lives".

Some poll findings were ignored. Asked which Iraqi leader they "do not trust at all", 10.3% said Ahmed Chalabi, compared with only 3.3% for Saddam Hussein. A large majority, 62%, think that "dealing with members of the previous government" should be "no priority at all". But will the coalition cancel plans for war crimes trials? This poll does not show that "the Iraqi people have spoken", but that many westerners continue to speak on their behalf.